Iteration and when to stop.
Unbounded computation may produce unbounded errors.
Solving equations by iteration and comparison to terminate it.
Newton’s method.
Order of convergence.
Why summing a Taylor series is problematic.

Ill Conditioning and Chaotic Simulations.
Role of partial derivatives and backwards stability.
Condition number when amenable to mathematical analysis;
Monte-Carlo exploration when not.
Finite-difference simulation and chaos in weather forecasting and Mandelbrot.